Directional Predictive Evidence for Collusion Auditing: A Pre-Registered, Sprint-Scale Test of the APTG-RL Design

Auditing multi-agent systems for collusion requires telling coordination apart from shared context, shared model tendencies and prompt-induced behaviour shifts. We test the APTG-RL design: a directional predictive-gain statistic between agents, a time-varying directed graph with temporal features, and a reinforcement-learning investigator that decides when to alert (its prompt-conditioned baseline is not exercised by the reported detectors). We build a three-seller repeated pricing game with four scripted collusion mechanisms, benign and shared-model negatives, and a seven-condition controlled design (C0–C6) of unilateral and common instruction perturbations, scripted collusion and benign policy shifts. Ten detectors, including the information-theoretic net-influence baseline, are compared on held-out episodes at thresholds fixed on validation negatives, under a pre-registered plan. A combined same-round-and-lagged directional gain beats symmetric mutual information (AUROC 0.839 vs. 0.755) but not lag-1 net influence (0.850); its strictly lagged part alone showed no clear advantage over symmetric MI (AUROC 0.704 vs. 0.755; difference inconclusive), and the parametric gain misses a parity-coded hidden channel that mutual information catches. The temporal-graph score did not help (0.740), and the RL investigator, which only rediscovered a “look at the first window” rule, bought lower delay and cost at lower recall. No statistically clear increase in false alarms was established under unilateral instruction perturbation, although small condition-level samples leave moderate increases possible. A small pilot with Claude Haiku 4.5 agents (720 decisions, 0 invalid) confirms that the perturbation shifts behaviour. This is simulator-only evidence at small scale; we report the nulls, the deviations we made, and the limits.